Monotonic piecewise cubic interpolation, with applications to ODE plotting

D.J. Higham

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Given a set of solution and derivative values, we examine the problem of constructing a piecewise cubic interpolant which reflects the monotonicity present in the data. Drawing on the theory of Fritsch and Carlson (1980), we derive a simple algorithm that, if necessary, adds one or two extra knots between existing knots in order to preserve monotonicity. The new algorithm is completely local in nature and does not perturb the input data. We show that the algorithm is particularly suited to the case where the data arises from the discrete approximate solution of an ODE.
LanguageEnglish
Pages287-294
Number of pages7
JournalJournal of Computational and Applied Mathematics
Volume39
Issue number3
DOIs
Publication statusPublished - 8 May 1992

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Monotonic
Interpolation
Interpolate
Knot
Monotonicity
Interpolants
Approximate Solution
Derivatives
Derivative
Necessary
Drawing

Keywords

  • Cubic polynomial
  • Hermite
  • interpolation
  • monotonicity
  • initial-value problem
  • numerical mathematics

Cite this

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Monotonic piecewise cubic interpolation, with applications to ODE plotting. / Higham, D.J.

In: Journal of Computational and Applied Mathematics, Vol. 39, No. 3, 08.05.1992, p. 287-294.

Research output: Contribution to journalArticle

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